Phase portraits of quadratic polynomial vector fields having a rational first integral of degree 2

We classify all the global phase portraits of the quadratic polynomial vector fields having a rational first integral of degree 2. In other words we characterize all the global phase portraits of the quadratic polynomial vector fields having all their orbits contained in conics. For such a vector field there are exactly 25 different global phase portraits in the Poincaré disc, up to a reversal of sense.     

The Center Problem for a Linear Center Perturbed by Homogeneous Polynomials

The centers of the polynomial differential systems with homogeneous polynomials have been studied for the degrees s = 2, 3, 4, 5. for s = 2, 3, and partially classified for s = 4, 5. In this paper we recall and we give new centers for s = 6, 7 a linear center perturbed by They are completely classified these results for s = 2, 3, 4, 5,     

Schwinger Formula Revisited

We apply the formal W.K.B. method in the complex plane to the quantum field theory to obtain the Schwinger formula for spin and spinless particles; i.e., we obtain the probability that the vacuum state remains unchanged in presence of a constant electric field. Finally, from Schwinger formula we calculate the probability that n pairs are produced.     

On the relation between protonium level shifts and nucleon-antinucleon scattering amplitudes

We study the Coulomb and threshold corrections to the low-energy scattering parameters for the proton-antiproton system, with numerical examples based on current optical models. Some commonly used expressions are shown to be inconsistent with our results. We check that the Trueman formula is valid for the level shifts of protonium, provided one takes properly into account the Coulomb corrections to the scattering lengths and volumes.     

New synthetic “tricks” using old reagents. A mild method for the conversion of RCONHR′ to RCONHR″

N-Alkyl-N-nitrosoamides, RCON(NO)R′, react with primary aliphatic amines (NH₂R″), in refluxing dichloromethane or at room temperature, to give RCONHR″ in 65–98% yields.     

Interactions of thiophenes and acidophilic,thermophilic bacteria

The growth and oxygen consumption of a variety of thermophilic, acidophilic bacteria in the presence of thiophene-2-carboxylate (T2C) and dibenzothiophene (DBT) have been determined. T2C was extremely toxic to the acidophiles in comparison with neutrophiles, but appeared to be degraded by a heterotrophicSulfolobus- like thermophile. DBT proved to be unstable at high temperatures, even in the absence of bacteria, and was not a substrate for the thermophiles.     

Linked crystallites in the conducting topmost layer of polymer bilayer films controlled by temperature: from micro- to nanocrystallites.

Temperature has great impact on the structure and size of the linked crystallites of the conducting topmost layer formed at the surface of a polycarbonate film via the reaction BEDT-TTF+IBr [BEDT-TTF=bis(ethylenedithio)tetrathiafulvalene]. We show that fine temperature control permits formation of a semiconducting topmost layer of alpha'-(BEDT-TTF)(2)(I(x)Br(1-x))(3) crystallites with either micro- or nanometre size, a result that opens a route to miniaturized conducting plastic materials.     

Regioselective cyclomanganation of Schiff bases. An unexpected effect of chloro substituents

In this paper we describe the synthesis of new metallacycles by the cyclomanganation reaction of benzyl-benzylidene-amines by using [MnMe(CO)₅] as metallating agent. These ligands can undergo metallation on different aromatic carbon atoms but no important differences have been found in the regioselectivity of the process, that can be related to the electronic effect of the substituents, and in all the cases studied the endo-cyclomanganated complexes of para-substituted imines have been obtained. The corresponding exo-metallacycles were obtained by reaction of [MnMe(CO)₅] on the imine 2,6-Cl₂C₆H₃CHNCH₂Ph and 2,4,6-Me₃C₆H₂CHNCH₂Ph, derived from 2,6-dichlorobenzaldehyde and 2,4,6-trimethylbenzaldehyde, respectively.The results described suggest that the mechanism of the cyclomanganation is similar to that of cyclopalladation and it can be proposed that cyclomanganation takes place by the formation of a four-centered transition state, involving the C-H and Mn-C_acetyl bonds, in the acetyl coordination complex formed in the first step of the reaction.     

Advantages of the Ns group in the reactions of N-SO2R inosines with benzylamine and with NH3

The reactivity of N¹-alkylsulfonyl- and N¹-arylsulfonyl-2′,3′,5′-tri-O-acetylinosine with benzylamine and with ¹⁵NH₃, regarding the attack on C2, has been shown to be in the order CF₃SO₂ (Tf) > 2,4-(NO₂)₂C₆H₃SO₂ (DNs) ? 4-NO₂C₆H₄SO₂ (pNs) ≈ C₆F₅SO₂ (PFBs) > 2-NO₂C₆H₄SO₂ (Ns) ? CH₃SO₂ (Ms) > 4-CH₃C₆H₄SO₂ (Ts) > 2,4,6-(CH₃)₃C₆H₂SO₂ (Mts). In spite of its intermediate reactivity, the Ns group is the most appropriate, since in this case the formation of by-products is minimised during the ring-opening and ring-closing steps of the process. Another advantage of the Ns group is thus disclosed.